Internet Appendix to “Should Derivatives Be Privileged in Bankruptcy?” PATRICK BOLTON and MARTIN OEHMKE∗ This Internet Appendix contains a number of additional results and details that were omitted from the main paper. Section I contains a detailed discussion of the results presented in Sections VI.A and VI.B of the main paper. Section II discusses a number of robustness issues related to the model setup.

I.

Derivation of Results in Sections VI.A and VI.B

This section contains a detailed discussion of the results presented in Sections VI.A and VI.B of the paper: the priority ranking in the presence of cross-netting when (i) basis risk and cash flow risk are systematic and (ii) basis risk and cash flow risk are idiosyncratic. Basis Risk and Cash Flow Risk Are Systematic: Consider first the case in which both cash flow risk and basis risk are systematic. In this case, when the representative counterparty observes the signal sH , it learns that all derivatives it has written will move against it, and thus a significant liability is added to its balance sheet. To preserve incentives, the counterparty must now post collateral in a margin account, which leads to deadweight costs. When derivatives are senior, the counterparty incurs an aggregate liability of X S if all derivatives simultaneously move against it (Z = Z H ). In this case, which occurs with probability 1 − θ, the counterparty has to post an amount ζS =

X S − AP Γ−P

(IA.1)

as collateral. When the derivative moves in favor of the counterparty, no collateral has to be posted. As a result, the ex ante zero-profit condition for the counterparty is given by

θxS − (1 − θ) X S − (1 − θ) (1 − Γ) ζ S = 0, ∗

(IA.2)

Citation format: Bolton, Patrick, and Martin Oehmke, Internet Appendix to “Should Derivatives Be Privileged in Bankruptcy?” Journal of Finance 70(6), 2353-2394, 2015, [DOI: 10.1111/jofi.12201].

1

where the term (1 − θ) (1 − Γ) ζ S reflects the expected deadweight cost of collateral that the counterparty is required to post when derivatives are senior. Now consider junior derivatives. When Z = Z H , the counterparty receives the payment xJ only if all firms obtain the high cash flow C1H (i.e., payment to the counterparty depends on the realization of the aggregate basis risk). Hence, the counterparty receives xJ only with probability [θ − (1 − θ) (1 − γ)]. When Z = Z L , the counterparty incurs an aggregate liability of X J and it must therefore post an amount ζJ =

X J − AP Γ−P

(IA.3)

of collateral. The ex ante zero-profit condition for the counterparty is then given by

[θ − (1 − θ) (1 − γ)] xJ − (1 − θ) X J − (1 − θ) (Γ − 1) ζ J = 0.

(IA.4)

Again, the term (1 − θ) (Γ − 1) ζ S reflects the expected deadweight cost of collateral. Not surprisingly, in this case the comparison of the junior and senior derivative regimes is analogous to the partial equilibrium analysis in the preceding section. Because RJ > RS , the required notional derivative position is higher under senior derivatives than under junior derivatives: X S > X J . This leads to a higher aggregate net liability for the counterparty, such that the required collateral is higher under senior derivatives than junior derivatives, ζ S > ζ J . This leads to higher deadweight costs under senior derivatives. Essentially, when cash flow risk and basis risk are perfectly correlated across firms, seniority for derivatives does not generate diversification benefits for the derivative counterparty. Hence, the only relevant efficiency consideration is to lower the size of the required derivative positions, which is achieved by making derivatives junior to debt in bankruptcy. Basis Risk and Cash Flow Risk Are Idiosyncratic: Suppose now that both cash flow risk and basis risk are idiosyncratic. Then the payoff to the representative derivative counterparty is deterministic. By the law of large numbers, a fraction θ of the counterparty’s derivative contract moves in favor of the counterparty (Z = Z H ), while a fraction 1 − θ moves out of favor (Z = Z L ). When derivatives are senior to debt, the balance sheet of the representative counterparty is thereby given

2

by A + θxS − (1 − θ) X S ,

(IA.5)

assuming that the counterparty is not required to post collateral, which we verify below. Given that the counterparty cannot make strictly positive profits in equilibrium, the following zero-profit condition must hold: A + θxS − (1 − θ) X S = A.

(IA.6)

The counterparty thus sets xS such that θxS − (1 − θ) X S = 0. Because its balance sheet is deterministic, the counterparty never has a net liability, which implies that the counterparty’s incentive constraint is always satisfied and no collateral has to be posted (ζ S = 0). An analogous argument applies when derivatives are junior to debt. In this case, the balance sheet of the counterparty (again assuming that no collateral has to be posted) is given by

A + [θ − (1 − θ) (1 − γ)] xJ − (1 − θ) X J ,

(IA.7)

taking into account the fact that the counterparty receives no payment from firms that receive C1L and owe xS to the counterparty. The counterparty’s zero-profit condition thus becomes

A + [θ − (1 − θ) (1 − γ)] xJ − (1 − θ) X J = A,

(IA.8)

and the counterparty sets xJ such that [θ − (1 − θ) (1 − γ)] xJ − (1 − θ) X J = 0. Also in this case, because its balance sheet is deterministic, the counterparty never has a net liability, which implies that the counterparty’s incentive constraint is always satisfied and no collateral has to be posted (ζ J = 0). Because ζ S = ζ J = 0, no deadweight costs arise for the counterparty, irrespective of the relative priority of debt and derivative contracts. Hence, while the pricing of the derivative contract differs depending on the bankruptcy regime (equations (IA.6) and (IA.8)), the relative priority ranking of debt and derivatives does not affect aggregate surplus.

3

II.

Robustness

To keep the analysis tractable we have considered the most stripped-down setting possible, with only two periods and two possible cash flow realizations at date 1. However, the main qualitative results hold in much more general settings. Note first that it is not essential to restrict the number of possible cash flow outcomes to only two. As shown by Faure-Grimaud (2000) and Povel and Raith (2004), when the firm’s cash flow at date 1 is drawn from a continuum of possible realizations, C1 ∈ [0, C¯1 ], with a probability density function h(C1 ), then the optimal financial contract also takes the form of a debt contract and has the following features. The firm can continue operating until date 2 if it repays the promised debt amount B ≤ C2 at date 1. If the firm repays an amount ρ < B, then it can continue to operate only with probability λ(ρ) = 1 −

B−ρ . C2

(IA.9)

This contract gives the firm an incentive to repay as much as it can (ρ = C1 ) at date 1 whenever its cash flow realization falls short of its total obligation B. Note that this contract has the same general properties as the contract we derived in the case of two cash flow outcomes: it leads to efficient continuation in all cash flow states C1 ≥ B, and it results in inefficient liquidation (with positive probability) in all cash flow states C1 < B. Moreover, the probability of inefficient liquidation increases in the repayment shortfall (B − C1 ). This result continues to hold when C2 is also random (for details, see Faure-Grimaud (2000) and Povel and Raith (2004)). As in the setting with only two possible cash flow realizations, it is straightforward to see that a derivative contract specifying payments contingent on a random variable Z that is negatively correlated with C1 can improve on the outcome without derivatives. Consider, for example, the case in which Z is continuously distributed on the support [Z, Z] and is perfectly negatively correlated with C1 , such that there is no basis risk. With a slight abuse of notation, let the support [Z, Z] be the same as the support of cash flows [0, C¯1 ]. Then a derivative contract such that X(C1 ) = B − C1 for all C1 < B and X(C1 ) = −α(C1 − B) for all C1 ≥ B (with α ∈ (0, 1)) would provide perfect insurance to the firm as in the setting with only two possible cash flow realizations. To break even,

4

the counterparty would set α such that Z

¯1 C

Z

B

(B − C1 )dH(C1 ).

(C1 − B)dH(C1 ) =

α

(IA.10)

0

B

In the presence of basis risk, the same general trade-off and qualitative result on the optimal priority ranking of debt and derivatives would obtain as in the case with two cash flow realizations, although the mathematical analysis would be considerably more involved. In particular, when the derivative counterparty and creditor have competing claims in a low-cash flow state (C1 < B), then the effect of giving seniority to the derivative contract is to raise the promised debt repayment B and therefore the firm’s demand for insurance via the derivative. As in the model with only two possible cash flows, this raises the deadweight cost of hedging by increasing collateral requirements for the derivative counterparty. Another simplification in our model is that the firm has a single investment of fixed size F . Our analysis can be extended to a situation in which cash flows are an increasing concave function of initial variable investment I: {C1L (I), C1H (I), C2 (I)}. In this more general setting, there would be an additional cost of giving priority to derivatives over debt: by raising the cost of funding for the firm, it would also result in lower investment. Similarly, the model can be extended to introduce corporate taxes and a tax shield benefit of debt, as is shown in Appendix B of the NBER working paper version of this article (NPER WP 17599). When the firm can obtain a tax shield benefit of debt it will generally issue more debt claims than it needs in order to finance the setup cost F . One may then wonder whether having senior derivatives may actually not be a benefit to the firm, as the higher promised debt repayment would provide the firm with a higher tax shield. We show, however, that this benefit is always outweighed by the higher deadweight cost of hedging. Finally, the analysis can be generalized to allow for costly outside equity financing. In our framework, the costs of outside equity could be, for example, auditing costs that arise when verifying realized cash flows. In this more general model, the firm may choose equity financing over debt financing if bankruptcy costs are too high. The costs of giving derivatives seniority over debt then no longer come only in the form of higher deadweight costs of hedging, but also from pushing the firm toward costly equity financing. The privileged bankruptcy treatment of derivatives would still be inefficient; only the specific form of the costly distortion would change.

5

REFERENCES Faure-Grimaud, Antoine, 2000, Product market competition and optimal debt contracts: The limited liability effect revisited, European Economic Review 44, 1823–1840. Povel, Paul, and Michael Raith, 2004, Optimal debt with unobservable investments, RAND Journal of Economics 35, 599–616.

6